However, in my case, the polarity is not reversed - red goes to positive and black goes to negative on the board. When plugged into the battery, the red wire from the battery connector is lined up with the red wire on the Crazyflie connector, and the black wires are lined up as well. I have upgraded to the latest firmware via the bootloader process, and have installed the latest driver for the PA dongle. I can connect to the drone and get flight data updates if I move the drone around manually via the CF client. It also shows the battery charge (although that fluctuates weirdly from time to time).

I have the additional issue that my XBox 360 controller doesn't seem to provide any input even with the XBox 360 profile connected when the drone is tethered via USB. But right now I just want it to turn on with battery power. The POST is fine - 5 rapid green blinks from M4, then periodic red blinks from M1, M2 and M3 solid blue.

I bought some replacement batteries and that cleared everything up. It seems like it was a faulty battery in my case. The only problem now is that, despite having a Flow Deck installed, it doesn't seem capable of level flight, so I can't really use it; it immediately flips upside down a few inches off the ground when controlled from a Python script, or starts drifting faster than I can correct for with a manual controller. I'll check other threads for possible solutions to that.